4.2.2.4. pde.grids.operators.polar_sym module¶
This module implements differential operators on polar grids
make a discretized laplace operator for a polar grid |
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make a discretized gradient operator for a polar grid |
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make a discretized divergence operator for a polar grid |
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make a discretized vector gradient operator for a polar grid |
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make a discretized tensor divergence operator for a polar grid |
- make_divergence(grid)[source]¶
make a discretized divergence operator for a polar grid
The polar grid assumes polar symmetry, so that fields only depend on the radial coordinate r. The radial discretization is defined as \(r_i = r_\mathrm{min} + (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\), where \(r_\mathrm{min}\) is the radius of the inner boundary, which is zero by default. Note that the radius of the outer boundary is given by \(r_\mathrm{max} = r_\mathrm{min} + N_r \Delta r\).
- Parameters
grid (
PolarSymGrid) – The polar grid for which this operator will be defined- Returns
A function that can be applied to an array of values
- Return type
- make_gradient(grid)[source]¶
make a discretized gradient operator for a polar grid
The polar grid assumes polar symmetry, so that fields only depend on the radial coordinate r. The radial discretization is defined as \(r_i = r_\mathrm{min} + (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\), where \(r_\mathrm{min}\) is the radius of the inner boundary, which is zero by default. Note that the radius of the outer boundary is given by \(r_\mathrm{max} = r_\mathrm{min} + N_r \Delta r\).
- Parameters
grid (
PolarSymGrid) – The polar grid for which this operator will be defined- Returns
A function that can be applied to an array of values
- Return type
- make_gradient_squared(grid, central=True)[source]¶
make a discretized gradient squared operator for a polar grid
The polar grid assumes polar symmetry, so that fields only depend on the radial coordinate r. The radial discretization is defined as \(r_i = r_\mathrm{min} + (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\), where \(r_\mathrm{min}\) is the radius of the inner boundary, which is zero by default. Note that the radius of the outer boundary is given by \(r_\mathrm{max} = r_\mathrm{min} + N_r \Delta r\).
- Parameters
grid (
PolarSymGrid) – The polar grid for which this operator will be definedcentral (bool) – Whether a central difference approximation is used for the gradient operator. If this is False, the squared gradient is calculated as the mean of the squared values of the forward and backward derivatives.
- Returns
A function that can be applied to an array of values
- Return type
- make_laplace(grid)[source]¶
make a discretized laplace operator for a polar grid
The polar grid assumes polar symmetry, so that fields only depend on the radial coordinate r. The radial discretization is defined as \(r_i = r_\mathrm{min} + (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\), where \(r_\mathrm{min}\) is the radius of the inner boundary, which is zero by default. Note that the radius of the outer boundary is given by \(r_\mathrm{max} = r_\mathrm{min} + N_r \Delta r\).
- Parameters
grid (
PolarSymGrid) – The polar grid for which this operator will be defined- Returns
A function that can be applied to an array of values
- Return type
- make_poisson_solver(bcs, method='auto')[source]¶
make a operator that solves Poisson’s equation
The polar grid assumes polar symmetry, so that fields only depend on the radial coordinate r. The radial discretization is defined as \(r_i = r_\mathrm{min} + (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\), where \(r_\mathrm{min}\) is the radius of the inner boundary, which is zero by default. Note that the radius of the outer boundary is given by \(r_\mathrm{max} = r_\mathrm{min} + N_r \Delta r\).
- Parameters
bcs (
Boundaries) – Specifies the boundary conditions applied to the field. This must be an instance ofBoundaries, which can be created from various data formats using the class methodfrom_data().method (str) – The chosen method for implementing the operator
- Returns
A function that can be applied to an array of values
- Return type
- make_tensor_divergence(grid)[source]¶
make a discretized tensor divergence operator for a polar grid
The polar grid assumes polar symmetry, so that fields only depend on the radial coordinate r. The radial discretization is defined as \(r_i = r_\mathrm{min} + (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\), where \(r_\mathrm{min}\) is the radius of the inner boundary, which is zero by default. Note that the radius of the outer boundary is given by \(r_\mathrm{max} = r_\mathrm{min} + N_r \Delta r\).
- Parameters
grid (
PolarSymGrid) – The polar grid for which this operator will be defined- Returns
A function that can be applied to an array of values
- Return type
- make_vector_gradient(grid)[source]¶
make a discretized vector gradient operator for a polar grid
The polar grid assumes polar symmetry, so that fields only depend on the radial coordinate r. The radial discretization is defined as \(r_i = r_\mathrm{min} + (i + \frac12) \Delta r\) for \(i=0, \ldots, N_r-1\), where \(r_\mathrm{min}\) is the radius of the inner boundary, which is zero by default. Note that the radius of the outer boundary is given by \(r_\mathrm{max} = r_\mathrm{min} + N_r \Delta r\).
- Parameters
grid (
PolarSymGrid) – The polar grid for which this operator will be defined- Returns
A function that can be applied to an array of values
- Return type